基于物理信息神经网络的燃烧化学微分方程求解

Solving combustion chemical differential equations via physics-informed neural network

为了有效地将湍流燃烧复杂的物理化学信息嵌入到物理信息神经网络(PINNs),选取湍流燃烧模拟中的2个典型场景案例,即刚性常微分方程ROBER问题及稳态射流火焰混合分数方程求解,探索PINNs在燃烧化学微分方程计算中的应用潜力.结果表明,对于零维刚性反应系统,利用PINNs模型可以较好地捕捉到系统的演化过程;对于稳态射流火焰,PINNs的预测解与传统的数值解有较好的一致性.残差点的选取对于燃烧化学领域内的复杂微分方程求解尤为重要,应基于具体的构型详细考虑.

Two typical cases including the stiff system of ordinary differential equations ROBER problem and the steady-state mixture fraction equation in jet flame were selected in order to efficiently embed the complex physicochemical information of turbulent combustion into physics-informed neural networks(PINNs). The potential of PINNs in solving combustion chemical differential equations was explored. Results show that the PINNs model can correctly capture the evolution of the zero-dimensional stiff reaction system. PINNs solution accorded well with the conventional numerical solution for steady jet flame. The selection of residual points was particularly important for solving complex differential equations in the field of combustion and chemistry, which should be considered based on the specific configuration in detail.